利用周期性cos(15π/8)=cos(15π/8-2π)=cos( -π/8)=cos (π/8)cos(14π/9) =cos(14π/9-2π)=cos(-4π/9)=cos(4π/9)已知0<π/8 <4π/9 <π/2 cosx在(0,π/2)上单调递减。所以cos(π/8)>cos(4π/9) 即os(15π/8)>cos(14π/9)
因为前者是(15/8)兀,后者是(14/9)兀,都是第三象限的角。余弦为负值。前者角度大,余弦绝对值小,所以反而大。